A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$5.50$, and bags of cookies cost $$4.00$, and sales equaled $$50.00$ in total. There were $3$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${5.5x+4y = 50}$ ${y = x+3}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+3}$ for $y$ in the first equation. ${5.5x + 4}{(x+3)}{= 50}$ Simplify and solve for $x$ $ 5.5x+4x + 12 = 50 $ $ 9.5x+12 = 50 $ $ 9.5x = 38 $ $ x = \dfrac{38}{9.5} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+3}$ to find $y$ ${y = }{(4)}{ + 3}$ ${y = 7}$ You can also plug ${x = 4}$ into $ {5.5x+4y = 50}$ and get the same answer for $y$ ${5.5}{(4)}{ + 4y = 50}$ ${y = 7}$ $4$ bags of candy and $7$ bags of cookies were sold.